The Mathematics of Criminal Behavior: Modeling and Experiments

In this era of "big data", Mathematics as it applies to
human behavior is becoming a much more relevant and penetrable topic
of research. This holds true even for some of the less desirable
forms of human behavior, such as crime. In this talk, I will discuss
the mathematical modeling of crime on various "scales" and using
many different mathematical techniques, as well as the results of
experiments
that are being performed to test the usefulness and accuracy of these
models.
This will include: models of crime hotspots at the scale of neighborhoods
-- in
the form of systems of PDEs and also statistical models adapted from
literature on
earthquake predictions -- along with the results of the model's application
within the LAPD; a model for gang retaliatory violence on the scale of
social
networks, and its use in the solution of an inverse problem to help solve
gang crimes; and a game-theoretic model of crime and punishment at the
scale of a society, with comparisons of the model to results of lab-based
economic experiments performed by myself and collaborators.